Distributed Structures, Sequential Optimization, and Quantization for Detection

In the design of distributed quantization systems, one inevitably confronts two types of constraints - those imposed by a distributed system's structure and those imposed by how the distributed system is optimized. Structural constraints are inherent properties of any distributed quantization system and are normally summarized by functional relationships defining the inputs and outputs of their component quantizers. The use of suboptimal optimization methods are often necessitated by the computational complexity encountered in distributed problems. This correspondence briefly explores the impact and interplay of these two types of constraints in the context of distributed quantization for detection. We introduce two structures that exploit interquantizer communications and that represent extremes in terms of their structural constraints. We then develop a sequential optimization scheme that maximizes the Kullback-Leibler divergence, takes advantage of statistical dependencies in the distributed system's output variables, and leads to simple parameterizations of the component quantization rules. We present an illustrative example from which we draw insights into how these constraints influence the quantization boundaries and affect performance relative to lower and upper bounds.